Answer :
To determine Wyatt's benefit rate, we'll break down each component of the benefits he receives, calculate their monetary value, and find the benefit rate. Let's go step-by-step.
### 1. Health Insurance
The total cost of health insurance is [tex]$10,000. Wyatt’s employer covers 60% of this cost. \[ 0.6 \times 10{,}000 = 6{,}000 \] So, the amount covered by the employer for health insurance is \$[/tex]6,000.
### 2. FICA (Federal Insurance Contributions Act)
FICA is 7.65% of Wyatt's salary. Wyatt’s annual salary is [tex]$65,000. \[ 0.0765 \times 65{,}000 = 4{,}972.5 \] So, the FICA contribution by the employer is \$[/tex]4,972.50.
### 3. Paid Time Off (PTO)
Wyatt receives 15 days of paid vacation. To find its value, we'll convert the days into a fraction of a year based on the number of working days in a year, which is approximately 260 days.
[tex]\[ \frac{15}{260} \times 65{,}000 = 3{,}750 \][/tex]
So, the value of PTO is \[tex]$3,750. ### 4. Retirement Matching The retirement matching is 6% of Wyatt's annual salary. \[ 0.06 \times 65{,}000 = 3{,}900 \] So, the retirement matching contribution is \$[/tex]3,900.
### 5. Total Benefit
Now, we'll sum up all these benefits to find the total benefit provided by the employer.
[tex]\[ 6{,}000 + 4{,}972.5 + 3{,}750 + 3{,}900 = 18{,}622.5 \][/tex]
So, the total benefit amount is \$18,622.50.
### 6. Benefit Rate
The benefit rate is calculated as the total benefit divided by the annual salary, expressed as a percentage.
[tex]\[ \left(\frac{18{,}622.5}{65{,}000}\right) \times 100 = 28.65\% \][/tex]
### 7. Rounding to Nearest Percentage Point
Finally, we round the benefit rate to the nearest whole number.
[tex]\[ 28.65\% \approx 29\% \][/tex]
Therefore, Wyatt's benefit rate is approximately [tex]\( \boxed{29\%} \)[/tex].
### 1. Health Insurance
The total cost of health insurance is [tex]$10,000. Wyatt’s employer covers 60% of this cost. \[ 0.6 \times 10{,}000 = 6{,}000 \] So, the amount covered by the employer for health insurance is \$[/tex]6,000.
### 2. FICA (Federal Insurance Contributions Act)
FICA is 7.65% of Wyatt's salary. Wyatt’s annual salary is [tex]$65,000. \[ 0.0765 \times 65{,}000 = 4{,}972.5 \] So, the FICA contribution by the employer is \$[/tex]4,972.50.
### 3. Paid Time Off (PTO)
Wyatt receives 15 days of paid vacation. To find its value, we'll convert the days into a fraction of a year based on the number of working days in a year, which is approximately 260 days.
[tex]\[ \frac{15}{260} \times 65{,}000 = 3{,}750 \][/tex]
So, the value of PTO is \[tex]$3,750. ### 4. Retirement Matching The retirement matching is 6% of Wyatt's annual salary. \[ 0.06 \times 65{,}000 = 3{,}900 \] So, the retirement matching contribution is \$[/tex]3,900.
### 5. Total Benefit
Now, we'll sum up all these benefits to find the total benefit provided by the employer.
[tex]\[ 6{,}000 + 4{,}972.5 + 3{,}750 + 3{,}900 = 18{,}622.5 \][/tex]
So, the total benefit amount is \$18,622.50.
### 6. Benefit Rate
The benefit rate is calculated as the total benefit divided by the annual salary, expressed as a percentage.
[tex]\[ \left(\frac{18{,}622.5}{65{,}000}\right) \times 100 = 28.65\% \][/tex]
### 7. Rounding to Nearest Percentage Point
Finally, we round the benefit rate to the nearest whole number.
[tex]\[ 28.65\% \approx 29\% \][/tex]
Therefore, Wyatt's benefit rate is approximately [tex]\( \boxed{29\%} \)[/tex].
